U.S. Sen. Scott Brown has moved into a narrow lead over rival Elizabeth Warren while his standing among Massachusetts voters has improved despite a year-long Democratic assault, a new UMass Lowell/Boston Herald poll shows.

The GOP incumbent is beating Warren by a 50-44 percent margin among registered Bay State voters, a turnaround from the last University of Massachusetts Lowell/Herald poll nine months ago that had the Democratic challenger leading by seven points. Among likely voters, Brown is leading the Harvard Law professor by a 49-45 percent margin, just within the poll’s 5.5 percent margin of error.

“I wasn’t too sure of him at first, but he’s been very independent,” said Jo Ann Dunnigan, a longtime Democrat and President Obama supporter from Fall River who participated in the poll, conducted Sept. 13-17.

Brown and Warren face off Oct. 1 in a debate sponsored by the Herald and UMass Lowell.

The poll, conducted by Princeton Survey Research Associates, shows nearly one in three Brown backers say they could change their mind before Election Day, compared to just 19 percent for Warren. But the poll, which started a week after the Democratic National Convention, finds no evidence of a “bounce” for Warren.

There also is some troubling news for the well-financed Warren campaign. Despite spending millions of dollars to tarnish Brown’s image, the GOP incumbent’s popularity has actually increased in the past nine months.

Brown is now viewed favorably by 57 percent of registered voters, up nine points from a UMass Lowell/Boston Herald poll conducted in December 2011. Brown’s unfavorable rating actually has dropped six points to 29 percent. He is also drawing 22 percent of voters who say they will vote for President Obama.

“I like the fact he grew up poor and knows what it means to have problems in your family,” said Valerica Stanta, a self-described independent from Haverhill who supports Obama and took part in the poll.

Warren is viewed favorably by 48 percent of voters — a 14-point increase from nine months ago — but her unfavorable rating has also increased seven points to 34 percent. And three of 10 registered voters say Warren’s views are “too liberal.”

Stanta said she has a “trust” problem with Warren because of her differing explanations for why she listed herself as an American Indian minority in law school directories. “When they avoid explaining exactly what is going on, I don’t feel comfortable,” Stanta said.

The UMass Lowell/Herald poll shows Brown also is benefiting from a huge gender gap — among men.

The GOP incumbent holds a 20-point lead among male voters, a huge advantage heading down the stretch. Warren, however, has not built up a similar advantage among female voters, holding just a seven-point lead over Brown. In the December 2011 poll, Warren held an 18-point lead among women.

That could reflect a major effort by Brown to target female voters, including a TV ad in which he folds laundry.

The poll also shows Brown continuing to hold a huge lead among self-described independent voters, 58 to 35 percent. He has also pulled even on an issue Warren has sought to make her own — fighting for the middle class. Asked which candidate would look out for the interests of the middle class, 46 percent of registered voters said Warren and 44 percent said Brown.

Self-described Democrats accounted for 28 percent of the poll respondents, and Democratic-leaning voters made up 55 percent of the poll.